Erhard Schmidt (13 January 1876 – 6 December 1959) was a Baltic German mathematician whose work significantly influenced the direction of mathematics in the twentieth century. Schmidt was born in

Tartu Tartu is the second largest city in Estonia after Tallinn. Tartu has a population of 97,759 (as of 2024). It is southeast of Tallinn and 245 kilometres (152 miles) northeast of Riga, Latvia. Tartu lies on the Emajõgi river, which connects the ...

(), in the Governorate of Livonia (now

Estonia Estonia, officially the Republic of Estonia, is a country in Northern Europe. It is bordered to the north by the Gulf of Finland across from Finland, to the west by the Baltic Sea across from Sweden, to the south by Latvia, and to the east by Ru ...

Mathematics

His advisor was

David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental idea ...

and he was awarded his doctorate from

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 ...

in 1905. His doctoral dissertation was entitled ' and was a work on

integral equations In mathematical analysis, integral equations are equations in which an unknown Function (mathematics), function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: f(x_1,x_2,x_3 ...

. Together with

he made important contributions to

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, Inner product space#Definition, inner product, Norm (mathematics ...

. Ernst Zermelo credited conversations with Schmidt for the idea and method for his classic 1904 proof of the Well-ordering theorem from an "

Axiom of choice In mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory. Informally put, the axiom of choice says that given any collection of non-empty sets, it is possible to construct a new set by choosing one element from e ...

", which has become an integral part of modern

set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...

. After the war, in 1948, Schmidt founded and became the first editor-in-chief of the journal '.

National Socialism

During

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

Schmidt held positions of authority at the

University of Berlin The Humboldt University of Berlin (, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick William III on the initiative of Wilhelm von Humbol ...

and had to carry out various

Nazi Nazism (), formally named National Socialism (NS; , ), is the far-right politics, far-right Totalitarianism, totalitarian socio-political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Germany. During H ...

resolutions against the Jews—a job that he apparently did not do well, since he was criticized at one point for not understanding the " Jewish question". At the celebration of Schmidt's 75th birthday in 1951 a prominent Jewish mathematician, Hans Freudenthal, who had survived the Nazi years, spoke of the difficulties that Schmidt faced during that period without criticism. Schmidt was, however, a conservative and a nationalist, and defended

Hitler Adolf Hitler (20 April 1889 – 30 April 1945) was an Austrian-born German politician who was the dictator of Nazi Germany from 1933 until Death of Adolf Hitler, his suicide in 1945. Adolf Hitler's rise to power, He rose to power as the lea ...

after Kristallnacht, telling

Issai Schur Issai Schur (10 January 1875 – 10 January 1941) was a Russian mathematician who worked in Germany for most of his life. He studied at the Humboldt University of Berlin, University of Berlin. He obtained his doctorate in 1901, became lecturer i ...

that "Suppose we had to fight a war to rearm Germany, unite with Austria, liberate the Saar and the German part of Czechoslovakia. Such a war would have cost us half a million young men. But everybody would have admired our victorious leader. Now, Hitler has sacrificed half a million Jews and has achieved great things for Germany. I hope some day you will be recompensed but I am still grateful to Hitler". Sanford L. Segal
Mathematicians Under the Nazis

Princeton University Press Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial ...

2003, Page 358.

Notes

References

* Reprinted in English translation as "Proof that every set can be well-ordered", van Heijenoort 1976, pp. 139–141. {{DEFAULTSORT:Schmidt, Erhard 1876 births 1959 deaths Scientists from Tartu People from Kreis Dorpat People of Baltic German descent 19th-century German mathematicians 20th-century German mathematicians Linear algebraists Academic journal editors University of Tartu alumni Emigrants from the Russian Empire to Germany Recipients of the National Prize of East Germany Presidents of the German Mathematical Society

Mathematics

National Socialism

See also

Notes

References